The phrase "are on one's tail" refers to a sense of urgency and pursuit. The antonyms for this phrase would be the opposite of being chased or followed closely. These antonyms may include "at a safe distance," "not being followed," or "free and clear." In such situations, there is no sense of danger or pressure, and individuals are free to move about without any fear of being caught or pursued. These antonyms may also include "unbothered," "unconcerned," or "undisturbed," suggesting a sense of calm and peace. Overall, these antonyms are a reminder that freedom and safety are valuable, and we should cherish them when we have them.